Some Mathematical Methods of PhysicsThis well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics. The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts useful in the treatment of continuous systems are also introduced. The final part examines approximation methods — including perturbation theory, variational methods, and numerical methods — relevant to addressing most of the problems of nature that confront applied physicists. Two Appendixes include background and supplementary material. 1960 edition. |
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Página 7
Such a matrix may be displayed, following (1.17), by an array with 11 rows and n columns. The elements m,, (= mu, mm, . . . , mm) lying on the principal diagonal of the matrix m are the diagonal elements of m ...
Such a matrix may be displayed, following (1.17), by an array with 11 rows and n columns. The elements m,, (= mu, mm, . . . , mm) lying on the principal diagonal of the matrix m are the diagonal elements of m ...
Página 11
... two distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its elements along the main diagonal (the elements Ikk) are FORMULATION OF THE PROBLEM AND DEVELOPMENT or NOTATION II.
... two distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its elements along the main diagonal (the elements Ikk) are FORMULATION OF THE PROBLEM AND DEVELOPMENT or NOTATION II.
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its elements along the main diagonal (the elements Ikk) are unity and all others are zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, ...
its elements along the main diagonal (the elements Ikk) are unity and all others are zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, ...
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Verify that AB = BA if A and B are both diagonal matrices of the same order; i.e., show that diagonal matrices commute with one another. 11. Show that if a matrix A commutes with another matrix B, then A commutes with any matrix of the ...
Verify that AB = BA if A and B are both diagonal matrices of the same order; i.e., show that diagonal matrices commute with one another. 11. Show that if a matrix A commutes with another matrix B, then A commutes with any matrix of the ...
Página 26
These results may be written in even more elegant form if the definition of a function f(A) of a diagonal matrix (with diagonal elements 2,) is introduced as1 [f(A)]u = f (it-)6” (218) Then the definition of s becomes As = sA (2.19) ...
These results may be written in even more elegant form if the definition of a function f(A) of a diagonal matrix (with diagonal elements 2,) is introduced as1 [f(A)]u = f (it-)6” (218) Then the definition of s becomes As = sA (2.19) ...
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applied approximate arbitrary base vectors basis Bessel function boundary conditions Chap chapter coefficients column commute complete consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector elements evaluate expansion find finite number first follows formula Fourier given Green’s function Hence Hermitian matrix Hermitian operator infinite integral Introduction inverse Laplacian linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company membrane method multiplication nonsingular normal normal matrix Note number of degrees obtained orthonormality conditions perturbation plane procedure QUANTUM MECHANICS relations representation result Ritz method satisfies satisfy scattering solve specified spherical spherical harmonics string Substitution theorem theory tion trial functions vanish variable vector space verified wave write written yields York zero
Información bibliográfica
| Título | Some Mathematical Methods of Physics Dover Books on Physics |
| Autores | Gerald Goertzel, Nunzio Tralli |
| Editor | Courier Corporation, 2014 |
| ISBN | 048679332X, 9780486793320 |
| Largo | 320 páginas |
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